Proposition: Prop. 10.019: Product of Rational Numbers is Rational

Euclid's Formulation

The rectangle contained by rational straight lines (which are) commensurable in length is rational. * For let the rectangle $AC$ have been enclosed by the rational straight lines $AB$ and $BC$ (which are) commensurable in length. * I say that $AC$ is rational.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9

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Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016